Process and Apparatus for Performing Initial Carrier Frequency Offset in an OFDM Communication System

ABSTRACT

A process for estimating the carrier frequency offset (CFO) for a Orthogonal Frequency Division Multiplex (OFDM) communication system, said process being performed in a receiver receiving a pilot sequence x=(x 0 , X 1 , X 2  . . . , X N-1 ) T , said process involving the step of determining a value of θ which maximizes the formula: (formula 1) where (formula 2, 3); Y is the diagonal matrix of main diagonal y; σ 2  is the noise power and Q is the channel time covariance matrix equal to 1/L I L , with I L  being the L×L identity matrix and L corresponding to the presumed length of the channel.

TECHNICAL FIELD

The invention relates to wireless digital communication and particularlyto a process for performing the estimation of a Carrier Frequency Offsetin a OFDM communication system, during the initial synchronization steps(i.e. prior to channel estimation).

BACKGROUND ART

The Orthogonal Frequency Division Multiplexing (OFDM) modulation is awidely developing technique in the field of wireless digitalcommunications thanks to the high possibilities offered by simplifieddigital signal processing based on Discrete Fourier Transformcomputations.

However, before a signal being received by a User Equipment (UE) may beproperly processed, a preliminary but critical synchronization step hasto be achieved including the estimation of the so-called CarrierFrequency Offset (CFO). Indeed, because of the mismatches of theinternal oscillators and also because of the Doppler effect resultingfrom mobile communications, the frequencies at the base station (eNodeB)and at the receiving terminal (UE) may differ, and such a differencemight be detrimental to the targeted transmission rate. In particular,if the CFO problem is not properly corrected, it is hazardous to performthe Discrete Fourier Transform stage at the receiver. In many systems,such as 3GPP-LTE, a first rough synchronization step is performed thanksto a primary synchronization sequence (PSS) which at this point is theonly known pilot sequence accessible to the receiver.

Before performing the next synchronization steps which require to usethe DFT block at the reception, it is critical to have a good CFOestimate; otherwise the performance of the subsequent synchronizationsteps might be heavily impaired.

A first, very well known, technique for estimating the CFO is disclosedby P. H. Moose in “A technique for orthogonal frequency-divisionmultiplexing frequency offset correction”, in IEEE Trans. onCommunications, vol. 42, no. 10, pp. 2908-2914, October 1994. Thetechnique is based on the use of a specific pilot sequence, a pilot OFDMsymbol composed of two identical vectors.

Such a technique presents the significant advantage of being workablewithout the knowledge of the channel characteristics and, therefore, ishighly useful during the first or coarse synchronization process whenonly limited information is available to the receiver. The cleardrawback of this well-known technique lies in the fact that therepetitive transmission of the Moose sequence is a large waste in termsof spectral efficiency since this sequence is not in general reusable toother synchronization purposes.

For such a reason in particular, the use of the Moose sequence has beenexcluded in some standards, such as the 3GPP-LTE for instance, and thereis only provided the so-called Primary Synchronization Sequence (PSS)for achieving the estimation of the CFO. In theory, by means of asystematic scanning of a dense discrete set of possible centralfrequencies, it is feasible to evaluate the CFO from the detection ofthe PSS but such a systematic scanning would require a great amount ofdigital processing resources and thus increase the processing costs ofthe receiver.

It is therefore desirable to have an alternative technique which canachieve CFO estimation with limited digital processing resources.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide a process forestimating the Carrier Frequency Offset (CFO) between a receiver and atransmitter in an OFDM communication system.

It is another object of the present invention to provide a process andapparatus which achieves CFO estimation on the basis of anypredetermined pilot sequence.

It is still another object of the present invention to provide a processand apparatus for performing CFO estimation on the basis of theso-called Primary Synchronization Signal (PSS).

It is still another object of the present invention to provide a processand apparatus for performing CFO estimation for a Long Term Evolution(LTE) communication system.

Those and other objects are achieved by means of the process accordingto the present invention which is performed in a communication devicereceiving a known (pilot) sequence x=(x₀, x₁, x₂ . . . , x_(N-1))^(T) oflength N.

The process involves the determination of a value of θ which maximizesthe formula:

${C(\theta)} = {{- d_{\theta}^{H}}Y^{H}{X\left( {{X^{H}X} + {\sigma^{2}Q^{- 1}}} \right)}^{- 1}\frac{1}{\sigma^{2}}X^{H}{Yd}_{\theta}}$

where

$X = \begin{pmatrix}x_{0} & x_{N - 1} & \cdots & x_{N - L - 1} \\x_{1} & x_{0} & \cdots & x_{N - L - 2} \\\vdots & \vdots & \vdots & \vdots \\x_{L - 2} & x_{L - 3} & \cdots & x_{N - 1} \\x_{L - 1} & x_{L - 2} & \cdots & x_{0} \\\vdots & \vdots & \vdots & \vdots \\x_{N - 1} & x_{N - 2} & \cdots & x_{N - L}\end{pmatrix}$${d_{\theta} = \left( {1,^{2\pi \frac{i\; \theta}{N}},\ldots,^{2\pi \frac{{({N - 1})}i\; \theta}{N}}} \right)^{T}};$

Y is the diagonal matrix of main diagonal y;

σ² is the noise power and Q is the assumed channel time covariancematrix.

In one embodiment, the Q matrix is set to be equal to 1/L I_(L), withI_(L) the L×L identity matrix and L corresponding to the presumed lengthof the channel (i.e. the approximate number of time samples over whichthe channel spreads).

Preferably, a dichotomic process is used for the purpose of estimatingthe value of θ which maximizes C(θ), such as a steepest descentalgorithm

In one embodiment, the process involves the steps of:

receiving an input signal y=(y₀, . . . , y_(N-1))^(T); detecting saidpilot signal;

computing an estimation of the variance σ² of the noise;

setting an estimate of the channel time covariance matrix Q, forinstance equal to 1/L I_(L),

computing a matrix A as follows:

$A = {Y^{H}{X\left( {{X^{H}X} + {\sigma^{2}Q^{- 1}}} \right)}^{- 1}\frac{1}{\sigma^{2}}X^{H}Y}$

where X is a pseudo-circulant matrix defined from said pilot signal

x=(x₀, x₁, x₂ . . . , x_(N-1))^(T) as follows:

$X = \begin{pmatrix}x_{0} & x_{N - 1} & \cdots & x_{N - L - 1} \\x_{1} & x_{0} & \cdots & x_{N - L - 2} \\\vdots & \vdots & \vdots & \vdots \\x_{L - 2} & x_{L - 3} & \cdots & x_{N - 1} \\x_{L - 1} & x_{L - 2} & \cdots & x_{0} \\\vdots & \vdots & \vdots & \vdots \\x_{N - 1} & x_{N - 2} & \cdots & x_{N - L}\end{pmatrix}$

Y is the diagonal matrix of main diagonal y;

σ² is the noise power.

computing the N−1 values of â in accordance with the formula:

${\overset{\sim}{a}}_{k} = {\sum\limits_{m = 1}^{N - k}\; A_{{k + m},m}}$

with A_(ij) the entries of matrix A.

computing the following vectors:

{tilde over (b)}

^(T)=

[ã ₁,2ã ₂, . . . ,(N−1)ã _(N-1)]

{tilde over (b)} _(ℑ) ^(T)=ℑ[ã ₁,2ã ₂, . . . ,(N−1)ã _(N-1)]

initializing a loop with the two variables:

θ_(min)=−½ and

θ_(max)=½

computing the value of

d={tilde over (b)}

^(T) ·s _(θ) +{tilde over (b)} _(ℑ) ^(T) ·c _(θ)

with

c _(θ) ^(T)=[ cos(2πθ/N), . . . , cos(2π(N−1)θ/N)]

s _(θ) ^(T)=[ sin(2πθ/N), . . . , sin(2π(N−1)θ/N)]

testing the sign of d;

if d is positive, then updating the value of θ_(min) as follows:

θ_(min)=(θ_(min)+θ_(max))/2

if d is negative, then updating the value of θ_(max) as follows:

θ_(max)=(θ_(min)+θ_(max))/2

repeating the preceding steps until the completion of the loop and, whenthe loop completes,

returning an estimation of said CFO in accordance with the formula:

{circumflex over (θ)}=[θ_(min)+θ_(max)]/2

The invention also provides a communication apparatus comprising areceiver for estimating the CFO for an OFDM communication system, whichcomprises:

a receiver for receiving an input signal comprising a pilot sequencex=(x₀, x₁, x₂ . . . , x_(N-1))^(T),

means for determining a value of θ which maximizes the formula:

${C(\theta)} = {{- d_{\theta}^{H}}Y^{H}{X\left( {{X^{H}X} + {\sigma^{2}Q^{- 1}}} \right)}^{- 1}\frac{1}{\sigma^{2}}X^{H}{Yd}_{\theta}}$

where

$X = \begin{pmatrix}x_{0} & x_{N - 1} & \cdots & x_{N - L - 1} \\x_{1} & x_{0} & \cdots & X_{N - L - 2} \\\vdots & \vdots & \vdots & \vdots \\x_{L - 2} & x_{L - 3} & \cdots & x_{N - 1} \\x_{L - 1} & x_{L - 2} & \cdots & x_{0} \\\vdots & \vdots & \vdots & \vdots \\x_{N - 1} & x_{N - 2} & \cdots & x_{N - L}\end{pmatrix}$${d_{\theta} = \left( {1,^{2\pi \frac{\; \theta}{N}},\ldots,^{2\pi \frac{{({N - 1})}\mspace{11mu} \theta}{N}}} \right)^{T}};$

Y is the diagonal matrix of main diagonal y;

σ² is the noise power and Q is the channel time covariance matrix.

The invention is particularly adapted for the estimation of the CFO fora 3GPP-LTE communication network and any type of mobile OFDM-basednetwork with no CFO-dedicated synchronization sequence.

DESCRIPTION OF THE DRAWINGS

Other features of one or more embodiments of the invention will best beunderstood by reference to the following detailed description when readin conjunction with the accompanying drawings.

FIG. 1 illustrates a first embodiment of a process in accordance withthe present invention.

FIG. 2 illustrates a second embodiment of a process in accordance withthe present invention.

FIG. 3 shows a comparison of the CFO estimates resulting from thetraditional Moose technique and the proposed invention, with N=128, L=3and L_(assumed) ε [3, 9]

FIGS. 4-6 show comparative results with the use of the steepest descentalgorithm of the invention, and with N=128, L=3, respectively with 3 to50 iterations.

FIG. 7 illustrates the impact of the choice of the particular pilotsequence for executing the process of the invention

DESCRIPTION OF THE PREFERRED EMBODIMENTS

It will now be described how to estimate the CEO from the sole knowledgeof any predetermined pilot sequence, for instance the so-called PrimarySynchronization Signal (PSS). However, it should be clear that the PSSis only indicated as an example and that other pilot sequences may beconsidered by the skilled man.

In the following, boldface lower-case symbols represent vectors, capitalboldface characters denote matrices (I_(N) is the N×N identity matrix).The Hermitian transpose is denoted (.)^(H). The set of N×M matrices overthe algebra A is denoted M(A, N, M). The operators det(X) and tr(X)represent the determinant and the trace of matrix X, respectively. Thesymbol E[.] denotes expectation.

Consider a pair of transmitter and receiver communicating through anoisy channel. The transmitter sends a data sequence x which thereceiver captures as a sequence y. The transmission vector channel isdenoted h. The noise is modeled as an additive white Gaussian (AWGN)sequence w. The extent of knowledge of the receiver, prior to datatransmission, is denoted I. In particular, the receiver frequencyreference is not perfectly aligned to that of the transmitter: thisintroduces a frequency offset θ whose knowledge to the receiver issummarized into the density function p(θ|I). By inductive reasoning, weprovide in the following an expression of the optimal inference thereceiver can make on (θ|y, I) which we apply to the example ofdata-aided CFO estimation in OFDM.

Consider an OFDM system of N subcarriers. The transmitter sends atime-domain pilot sequence x=(x₀, . . . , x_(N-1))^(T) (cyclic prefixexcluded), received as a sequence y=(y₀, . . . , y_(N-1))^(T) (cyclicprefix discarded). The transmission channel is discretized in L tapsh=(h₀, . . . , h_(L-1))^(T) and the AWGN noise w=(w₀, . . . ,W_(N-1))^(T) has entries of variance E[Iw_(k)|²]=σ². For the sake ofsimplicity, it will not be considered below the information contained inthe cyclic prefixes. Let θ represent the CFO to be estimated at thereceiver normalized to the subcarrier spacing, i.e. θ=1 is a frequencymismatch of one subcarrier spacing.

A CFO produces in OFDM a simple phase rotation of all transmittedtime-domain symbols x_(k) of an angle 2πkθ/N. While it seems feasible totrack the CFO in the time domain when the transmitted pilot sequencex—for instance the PSS—is assumed to be known, it should be noticed thatchannel estimation is not accessible to the UE during the initialsynchronization step, thus preventing direct deciphering of the impactof the channel on the time-domain symbols.

It is proposed to consider the maximum a posteriori value for θ giventhe received signal y defined as

y=Hx+n  (1)

where H is the circulant matrix of the time-domain OFDM channel (itsfirst row is h) and n the white Gaussian noise process.

This classical model can be rewritten

y=Xh+n  (2)

where h is composed of the L time-domain taps of the channel responseand X is the pseudo-circulant matrix defined as

$X = \begin{pmatrix}x_{0} & x_{N - 1} & \cdots & x_{N - L - 1} \\x_{1} & x_{0} & \cdots & X_{N - L - 2} \\\vdots & \vdots & \vdots & \vdots \\x_{L - 2} & x_{L - 3} & \cdots & x_{N - 1} \\x_{L - 1} & x_{L - 2} & \cdots & x_{0} \\\vdots & \vdots & \vdots & \vdots \\x_{N - 1} & x_{N - 2} & \cdots & x_{N - L}\end{pmatrix}$

It is assumed that the CFO is known to be comprised in the set θε[−½,½], where θ is normalized to the subcarrier spacing. We want to maximizethe probability p(θ|y).

One may assume uniform prior distribution of p(θ) in the set θε[−½, ½],then the maximization problem is concave in the variable θ and thereforecan be solved by steepest descent algorithms. After computation, it hasbeen observed that maximizing p(θ|y) is equivalent to maximize thefunction C(θ) defined as

${C(\theta)} = {{- d_{\theta}^{H}}Y^{H}{X\left( {{X^{H}X} + {\sigma^{2}Q^{- 1}}} \right)}^{- 1}\frac{1}{\sigma^{2}}X^{H}{Yd}_{\theta}}$

where

$X = \begin{pmatrix}x_{0} & x_{N - 1} & \cdots & x_{N - L - 1} \\x_{1} & x_{0} & \cdots & X_{N - L - 2} \\\vdots & \vdots & \vdots & \vdots \\x_{L - 2} & x_{L - 3} & \cdots & x_{N - 1} \\x_{L - 1} & x_{L - 2} & \cdots & x_{0} \\\vdots & \vdots & \vdots & \vdots \\x_{N - 1} & x_{N - 2} & \cdots & x_{N - L}\end{pmatrix}$${d_{\theta} = \left( {1,^{2\pi \frac{\mspace{11mu} \theta}{N}},\ldots,^{2\pi \frac{{({N - 1})}\; \theta}{N}}} \right)^{T}};$

Y is the diagonal matrix of main diagonal y;

σ² is the noise power.

where X is the pseudo-circulant matrix defined above, with a firstcolumn comprising the any pilot synchronization sequence x=(x₀, x₁, x₂ .. . , x_(N-1))^(T) (for instance the PSS), and the next columncomprising the circular permutation of the elements of vector x, ievector (x_(N-1), x₀, x₁, . . . x_(N-2))^(T), and the next one comprisingthe next consecutive circular permutation (x_(N-2), x_(N-1), x₀, . . . ,x_(N-3))^(T) and so on . . . .

The matrix Q is the channel time covariance matrix which is assumed tobe known. In one particular embodiment, one sets Q=1/L I_(L), with I_(L)being the L×L identity matrix and L corresponding to the presumed lengthof the channel. It should be noticed that, generally speaking, L is notknown a priori, but it has been advantageously observed that, to someextent, any non-trivial predetermined choice for L (and quite possiblywrong) does not alter much the results and the efficiency of the CFOestimation process. Therefore, the optimal maximum a priori solutionsimply consists in finding the value θ that maximizes C(θ).

I. Description of Embodiments

With respect to FIG. 1, there is now described the basic steps which areinvolved in the CFO estimation process in accordance with the presentinvention.

The process is executed in any receiver of a OFDM communication system,receiving an input signal y=(y₀, . . . , Y_(N-1))^(T) in a step 11.

Then, the process proceeds with a step 12 consisting in the detection ofthe PSS pilot signal.

In a step 13, the process computes an estimation of the Signal to NoiseRatio

(SNR) and therefore an evaluation of variance of the noise σ². Suchevaluation is achieved by techniques and algorithms which are well knownto a skilled man and which will not be developed with more details. Forinstance, the pilot sequence may be used for performing such evaluation.

In a step 14, the process proceeds with the computation of

${C(\theta)} = {{- d_{\theta}^{H}}Y^{H}{X\left( {{X^{H}X} + {\sigma^{2}Q^{- 1}}} \right)}^{- 1}\frac{1}{\sigma^{2}}X^{H}{Yd}_{\theta}}$

where

$X = \begin{pmatrix}x_{0} & x_{N - 1} & \cdots & x_{N - L - 1} \\x_{1} & x_{0} & \cdots & X_{N - L - 2} \\\vdots & \vdots & \vdots & \vdots \\x_{L - 2} & x_{L - 3} & \cdots & x_{N - 1} \\x_{L - 1} & x_{L - 2} & \cdots & x_{0} \\\vdots & \vdots & \vdots & \vdots \\x_{N - 1} & x_{N - 2} & \cdots & x_{N - L}\end{pmatrix}$${d_{\theta} = \left( {1,^{2\pi \frac{\; \theta}{N}},\ldots,^{2\pi \frac{{({N - 1})}\; \theta}{N}}} \right)^{T}};$

Y is the diagonal matrix of main diagonal y;

σ² is the noise power and Q=1/L I_(L).

and identifies the particular value of θ that maximizes C(θ).

In one particular embodiment, a processing loop is initiated for thepurpose of testing different values of θ and thus identifying theparticular value which maximizes C(θ).

Alternatively, it has been observed that C(θ) is concave and therefore adichotomy algorithm can be advantageously used for achieving a fastcomputation of the CFO estimation.

Once determined, the process returns in a step 15 the particular valueidentified in step 14 as being the estimated CFO.

As it will be apparent to the skilled man, the process which wasdescribed above can be embodied by means of different and numerousalgorithms. In addition, it will be clear to the skilled man that theformula above may take various formal presentations showing equivalentcomputations.

With respect to FIG. 2, there will now be described a second embodimentof the invention which requires limited digital processing resources.

The second embodiment includes steps 21-23 which are identical to steps11-13 of FIG. 1.

Therefore, after the computation of the value of σ², the processproceeds with a step 24 where the value of channel time covariancematrix Q is being set.

In one embodiment, the Q matrix is predetermined. Clearly, the sameassumption made in FIG. 1 may be applicable, for instance Q=1/L I_(L).

With the assumption made on matrix Q, the process then proceeds to astep 25 where the following matrix A (comprising elements a_(n,m)) iscomputed:

$A = {Y^{H}{X\left( {{X^{H}X} + {\sigma^{2}Q^{- 1}}} \right)}^{- 1}\frac{1}{\sigma^{2}}X^{H}Y}$

in which

$X = \begin{pmatrix}x_{0} & x_{N - 1} & \cdots & x_{N - L - 1} \\x_{1} & x_{0} & \cdots & X_{N - L - 2} \\\vdots & \vdots & \vdots & \vdots \\x_{L - 2} & x_{L - 3} & \cdots & x_{N - 1} \\x_{L - 1} & x_{L - 2} & \cdots & x_{0} \\\vdots & \vdots & \vdots & \vdots \\x_{N - 1} & x_{N - 2} & \cdots & x_{N - L}\end{pmatrix}$

where X is the pseudo-circulant matrix defined above,

Y is the diagonal matrix of main diagonal y;

σ² is the noise power.

In the case of PSS for LTE, the size of the A matrix is 64×64.

In one particular embodiment, the process only computes half of matrix Asince only the upper right coefficients A_(n,m) with n>m, need to beknown for the remaining part of matrix A as it will be apparent below.

In a step 26, the process then proceeds with the computation of the N−1values of â_(k) given by the following formula:

${\overset{\sim}{a}}_{k} = {\sum\limits_{m = 1}^{N - k}\; A_{{k + m},m}}$

Then, in a step 27, the process proceeds with the computation of the twofollowing vectors:

{tilde over (b)}

^(T)=

[ã ₁,2ã ₂, . . . ,(N−1)ã _(N-1)]

{tilde over (b)} _(ℑ) ^(T)=ℑ[ã ₁,2ã ₂, . . . ,(N−1)ã _(N-1)]

Then, in a step 28, the process enters into a loop and, in a step 29,initializes the following two variables:

θ_(min)=−½ and

θ_(max)=½

The process then proceeds with a step 30 where the value of d (thederivative of C(θ) in point θ) is computed:

d={tilde over (b)}

^(T) ·s _(θ) +{tilde over (b)} _(ℑ) ^(T) ·c _(θ)

with

c _(θ) ^(T)=[ cos(2πθ/N), . . . , cos(2π(N−1)θ/N)]

s _(θ) ^(T)=[ sin(2πθ/N), . . . , sin(2π(N−1)θ/N)]

Then, in a step 31, a simple test is performed in order to determinewhether d is positive or negative. Indeed, it has been observed thatfunction C(θ) is concave between (−½, ½), what opens the opportunity ofa simple test on the sign of d for determining the maximum value ofC(θ).

If d is found to be positive, then the process proceeds with a step 32where the value of θ_(min) is updated as follows:

θ_(min)=(θ_(min)+θ_(max))/2

and the process then proceeds to step 34

Conversely, if d is negative, then the process proceeds to a step 33where the value of θ is updated as follows:

θ_(max)=(θ_(min)+θ_(max))/2

The process then proceeds to a step 34 which is a new test on the end ofthe loop. If the loop is not terminated, then the process proceeds againto step 28.

If the loop is terminated, then the process proceeds with a step 35where the estimated value of the CFO is computed as follows:

{circumflex over (θ)}_(min)+[θ_(min)+θ_(max)]/2

The process then completes.

II. SIMULATION AND RESULTS

In the following, one may consider following we consider an OFDMtransmission with N=128 subcarriers. We assume perfect timing offsetalignment between the base station and the receiving terminal. A CFOmismatch θ is introduced. The receiver only knows that θε[−½, ½].

FIG. 3 shows a comparison of the CFO estimates resulting from thetraditional Moose technique and the proposed invention, with N=128, L=3and L_(assumed) ε[3, 9]. One considers a double-half sequence suggestedby Moose and the proposed method is compared against the Moose'scorrelation algorithm on 20,000 channels and CFO realizations (θ isuniformly distributed in [−½, ½]). The channel length is set to L=3,while the a priori on the channel length is either considered known,i.e. L_(assumed)=3, or wrongly estimated, here L_(assumed)=9. Therespective performances are analyzed in terms of average quadratic errorE[({circumflex over (θ)}−θ)²]

There is observed a significant performance gain provided by theproposed invention, especially in low SNR regime. It can be seen thatthe invention is indeed more able to cope with the noise impairmentwhich is more thoroughly modelled than in Moose's algorithm. Note alsothat a wrongly assigned prior p(θ|I) on the channel realization does notlead to critical performance decay; in the high SNR region, it is almostunimportant.

FIGS. 4-6 show the performance of the steepest descent algorithm whichwas described above. The system parameters are the same as in theprevious simulation, with a correct prior L_(assumed)=3 on the channellength at the receiver. The termination constraint is simply the numberof iterations k of the inner loop, which we limit to k=3, k=5, k=10 andk=50. It is observed that saturations appear for k<+∞, which areexplained by the systematic error introduced by the minimal step size2^(−k) in the iteration loop. For k>10, the performance plots (which wedid not provide for clarity) fit the plot k=50 in the −15 dB to 10 dBSNR range. Note also that the saturated standard deviation (defined asE[({circumflex over (θ)}−θ)²]^(1/2)) for k=5 is around 1% of thesubcarrier spacing, which corresponds to the maximum allowable CFOmismatch in most OFDM systems. Therefore, 5 iterations might besufficient to ensure a reliable estimation of the CFO.

FIG. 7 illustrates the impact of the choice of the particular pilotsequence for executing the process of the invention. Moose's randomlygenerated double-half pilot sequences as well as QPSK random sequencesare compared against the primary and secondary synchronization sequences(PSS, SSS) from the 3GPPLong Term Evolution standard. There is observeda large performance difference between those two types of pilots. Thisis simply due to the fact that both PSS and SSS are not of constantmodulus over time; this makes part of the signal more sensible to noiseand part of the signal less sensible to noise, but in average, thisleads to less efficient pilots in terms of CFO estimation. It should benoticed that also Moose's sequence is in no way better than any randomlygenerated sequence, which demystifies the original insightful idea fromMoose.

Applications of the Invention

This invention fits typically the needs of the 3GPP-LTE standard forwhich no sequence dedicated to CFO estimation is provided. Due to itsgenerality, this method can be applied in many OFDM systems which seekfor CFO estimation while not having access to the channel information.Since this scheme has a complexity which scales with the number ofiterations of the algorithm, it can be adapted to rough low consumptionestimates at the receiver as well as thin higher consumption estimatesat the base station.

The invention is particularly adapted to the Long Term Evolutionstandard, during the PSS to SSS synchronization phases.

The invention provides CFO estimation process prior to channelestimation in OFDM for any available pilot sequence. This is a veryadvantageous effect which was not known with prior art techniques: usualCFO techniques come along with a dedicated sequence. With the newtechnique which is proposed, there is no need of any specific sequence.Furthermore, it has been observed that the process is particularlyeffective when the sequence is composed of symbols having constantamplitude. It is then more advantageous to run this method on the mostappropriate pilots.

This invention eliminates the problem of initial synchronization priorto channel estimation. It can also help estimating the CFO from signalscoming from interfering base stations whose channels have not beenestimated. It is believed that no such general pilot-independent schemehas ever been proposed in the OFDM contest.

Furthermore, it has been observed that the technique described aboveshows better performance than the classical ad-hoc techniques based onthe first derivations of Moose. In the maximum a posteriori performanceviewpoint, it has even been proved that that technique is optimal.

1. A process for estimating the carrier frequency offset (CFO) for aOrthogonal Frequency Division Multiplex (OFDM) communication system,said process being performed in a receiver receiving a pilot sequencex=(x₀, x₁, x₂ . . . , x_(N-1))^(T), said process involving the step ofdetermining a value of θ which maximizes the formula:${C(\theta)} = {{- d_{\theta}^{H}}Y^{H}{X\left( {{X^{H}X} + {\sigma^{2}Q^{- 1}}} \right)}^{- 1}\frac{1}{\sigma^{2}}X^{H}{Yd}_{\theta}}$where $X = \begin{pmatrix}x_{0} & x_{N - 1} & \cdots & x_{N - L - 1} \\x_{1} & x_{0} & \cdots & X_{N - L - 2} \\\vdots & \vdots & \vdots & \vdots \\x_{L - 2} & x_{L - 3} & \cdots & x_{N - 1} \\x_{L - 1} & x_{L - 2} & \cdots & x_{0} \\\vdots & \vdots & \vdots & \vdots \\x_{N - 1} & x_{N - 2} & \cdots & x_{N - L}\end{pmatrix}$${d_{\theta} = \left( {1,^{2\pi \frac{\mspace{11mu} \theta}{N}},\ldots,^{2\pi \frac{{({N - 1})}\mspace{11mu} \theta}{N}}} \right)^{T}};$Y is the diagonal matrix of main diagonal y; σ² is the noise power and Qis the channel time covariance matrix.
 2. The process according to claim1 wherein the said matrix Q is set to be equal to 1/L I_(L), with I_(L)being the L×L identity matrix and L corresponding to the presumed lengthof the channel.
 3. The process according to claim 1 wherein—a dichotomyprocess is used for estimating the value of θ which maximizes C(θ). 4.The process according to claim 1 wherein the said matrix Q iscontextually determined from the physical location of the receiver. 5.The process according to claim 1, comprising the steps of: receiving(21) an input signal y=(y₀, . . . , y_(N-1))^(T); detecting (22) saidpilot signal; computing (23) an estimation of the variance of the noiseσ²; setting an estimation (24) of the channel time covariance matrix Q;computing elements A_(n,m) of a A matrix defined as follows:$A = {Y^{H}{X\left( {{X^{H}X} + {\sigma^{2}Q^{- 1}}} \right)}^{- 1}\frac{1}{\sigma^{2}}X^{H}Y}$where X is a pseudo-circulant matrix defined from said pilot signalx=(x₀, x₁, x₂ . . . , x_(N-1))^(T) as follows: $X = \begin{pmatrix}x_{0} & x_{N - 1} & \cdots & x_{N - L - 1} \\x_{1} & x_{0} & \cdots & X_{N - L - 2} \\\vdots & \vdots & \vdots & \vdots \\x_{L - 2} & x_{L - 3} & \cdots & x_{N - 1} \\x_{L - 1} & x_{L - 2} & \cdots & x_{0} \\\vdots & \vdots & \vdots & \vdots \\x_{N - 1} & x_{N - 2} & \cdots & x_{N - L}\end{pmatrix}$ Y is the diagonal matrix of main diagonal y; σ² is thenoise power computing (26) the N−1 values of â_(k) in accordance withthe formula:${\overset{\sim}{a}}_{k} = {\sum\limits_{m = 1}^{N - k}\; A_{{k + m},m}}$computing (27), the following vectors:{tilde over (b)}

^(T)=

[ã ₁,2ã ₂, . . . ,(N−1)ã _(N-1)]{tilde over (b)} _(ℑ) ^(T)=ℑ[ã ₁,2ã ₂, . . . ,(N−1)ã _(N-1)]initializing (29) a loop with the two variables: θ_(min)=−½ andθ_(max)=½ computing (30) the value ofd={tilde over (b)}

^(T) ·s _(θ) +{tilde over (b)} _(ℑ) ^(T) ·c _(θ)withc _(θ) ^(T)=[ cos(2πθ/N), . . . , cos(2π(N−1)θ/N)]s _(θ) ^(T)=[ sin(2πθ/N), . . . , sin(2π(N−1)θ/N)] testing (31) the signof d; if d is positive, then updating (32) the value of θ_(min) asfollows:θ_(min)=(θ_(min)+θ_(max))/2 if d is negative, then updating (33) thevalue of θ_(max) as follows:θ_(max)=(θ_(min)+θ_(max))/2 repeating step 29-33 until the completion ofsaid loop being determined by any predefined stopping requirement);completing (35) said process and returning an estimation of said CFO inaccordance with the formula:{circumflex over (θ)}=[θ_(min)+θ_(max)]/2
 6. The process according toclaim 5 wherein only the upper right coefficients A_(n,m) with n>m, arebeing computed during step
 26. 7. The process according to claim 1,wherein the said pilot sequence is a Primary Synchronization Signal. 8.The process according to claim 1, wherein the said receiver is a3GPP-LTE communication system.
 9. An apparatus for an OrthogonalFrequency Division Multiplexing communication system comprising: areceiver for receiving an input signal comprising a pilot sequencex=(x₀, x₁, x₂ . . . , x_(N-1))^(T), means for determining a value of θwhich maximizes the formula:${C(\theta)} = {{- d_{\theta}^{H}}Y^{H}{X\left( {{X^{H}X} + {\sigma^{2}Q^{- 1}}} \right)}^{- 1}\frac{1}{\sigma^{2}}X^{H}{Yd}_{\theta}}$where $X = \begin{pmatrix}x_{0} & x_{N - 1} & \cdots & x_{N - L - 1} \\x_{1} & x_{0} & \cdots & X_{N - L - 2} \\\vdots & \vdots & \vdots & \vdots \\x_{L - 2} & x_{L - 3} & \cdots & x_{N - 1} \\x_{L - 1} & x_{L - 2} & \cdots & x_{0} \\\vdots & \vdots & \vdots & \vdots \\x_{N - 1} & x_{N - 2} & \cdots & x_{N - L}\end{pmatrix}$${d_{\theta} = \left( {1,^{2\pi \frac{\mspace{11mu} \theta}{N}},\ldots,^{2\pi \frac{{({N - 1})}\mspace{11mu} \theta}{N}}} \right)^{T}};$Y is the diagonal matrix of main diagonal y; σ² is the noise power and Qis the channel time covariance matrix.
 10. The apparatus according toclaim 9 wherein the said matrix Q is set to be equal to 1/L I_(L), withI_(L) being the L×L identity matrix and L corresponding to the presumedlength of the channel.
 11. The apparatus according to claim 9 comprisingmeans for performing a dichotomic computation of the value of θ whichmaximizes C(θ).
 12. The apparatus according to claim 9, wherein the saidpilot sequence is a Primary Synchronization Signal.
 13. The apparatusaccording to claim 1, wherein the said receiver is a 3GPP-LTEcommunication system.
 14. A User Equipment comprising means forperforming the process as defined by claim 1.